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Past Seminar

Title              :

Integrable and Exactly Solvable models with Balanced Loss and Gain

Speaker         : Debdeep Sinha, Visva-Bharati University
Date                : June 03, 2019
Time               : 3:30 PM
Venue            : Room 3307
Abstract        :

A Hamiltonian formulation of generic many-particle systems with space-dependent balanced loss and gain coefficients will be presented. It will be shown that using a suitable choice of coordinates, the Hamiltonian can always be reformulated as a many-particle system in the background of a pseudo-Euclidean metric and subjected to an analogous inhomogeneous magnetic field with a functional form that is identical with space-dependent loss/gain co-efficient. Partially integrable systems will be presented for two distinct cases, namely, systems with (i) translational symmetry or (ii) rotational invariance in a pseudo-Euclidean space. Quantization of the Hamiltonian will also be discussed with the construction of the integrals of motion for specific choices of the potential and gain-loss coefficients. A few exact solutions for both the cases will be presented for specific choices of the potential and space-dependent gain/loss coefficients. This will include a coupled chain of nonlinear oscillators and a many particle Calogero type model with four-body inverse square plus two-body pair-wise harmonic interactions. A few quasi-exactly solvable models admitting bound states in appropriate Stoke wedges will also be discussed.



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